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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1006, page id 1815201908:1063
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1006
N GVLA CXLEHDR
AICOCOrpUS CF TTKD AB, ma
us cepamide quae hc sub bali re-
ctangula M C L. in alticudine BC.
Demonstratio.
TOrpuS CFFTKD AB eAt aquale py.
ramta (ub basi guxe sic aequalis lupert
ciebus CFHT, RCFTI, XO AD e sub
alcirudine BC, ve pacet ex dilcursu 62. hu-
ius, sed superHicieS C F FI, R G F FI, ROAD
maiores lunc rectangulo M CL, VE PateT eX
42. luius. ergo prramis, cuius basis rectan-
Gulum MCF, alcicudo reroBC, minot
eA prramide, cuius basis sunc plana praedi
cta et alcitudo BC, ad eoque criam minon
CACOrPOrE CFHKD AB. Quod eracde
monstrandum.
PROPOSITIO LXVIII.
beacaqualem rectansulo IA K, alcicudinem vero A F, Cemidiametrum.
Demonstratio.
Veacurenim EF qua trnormalis ad ali-
quodlacus polygoni, verbi zraria, BC, cis
rectus ex hrpochelicxlindrus sic, Facile demo
trabieur F L comunéese alcicudine prrami-
du, in quas corpus inscripeum ABFG HDP.
relolui porest. eric ergo prramis cuius bas lC
equalis superticicbus ABF, BCGF, CDHIC
alcirudo aurem F L, aequale inscripro corpoc
ABFGFIDE rrigutari. sunc aurem plana
ABF, BC CF, CDHTC aequaliaa rectano.
I0 Cx TB, AR. ergo prramis cuius balis est
rectangulum IB, AK. alcicudo F L, aGuAEUE
CEIAI COTPOTIINTCTIPIO ABEGFIDF. Prra-
mis vero sub balirectanguta I A R, X alcieu-
dine AF. haber balim maiorem quam sic re-
etangulum IB, AK, de habec alcicudinem AF
maiorem alcicudino F. C; igicur prramis sut
bal rectansula IB, AR, ex alcicudinc P L,
minor est prramide cuius bats est rectongu.
tum PAK, alcititdo aUTCM AF. ergO X COF-
DuS ABF GHID F infcripium ungula minus
prramide habenee Basim Actangulum IAR, d alticudinem A L lemidiame
a d
custacum EDHTFA, Cinlcribatur polygonum ABC D regu-
lare qualecunque circulari segmento BACOS AFD, _ secundum latera
Aca hcrngula qualis in praecedenr AC I, de segmenrum eodem mo-
polygoni plana ponantur axi parallela quarum communes interlectiones
cum plano ellipricoLInE AF, F C, CHI, ponacurque DIE normalis ad AI.
cerdlli.
Dico corpus inscriprum ongula minus esse prramide quae balim ha-
PR C
rum. uod erac demonstrandum.